Gregory K. Miller

Probability

Modeling and Applications to Random Processes

• Gebundenes Buch

Produktbeschreibung

Written by an enthusiastic educator known for his dynamic teaching, Probability: Modeling and Applications to Random Processes focuses on modeling outcomes of random variables and random processes. Filling the need for a solid introductory texts on probability and stochastic processes which explain the material clearly, the bookÕs central point is squarely that of the basic probability laws and modeling with probability distributions while exploring their applications and links to random phenomena.

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Improve Your Probability of Mastering This Topic

This book takes an innovative approach to calculus-based probability theory, considering it within a framework for creating models of random phenomena. The author focuses on the synthesis of stochastic models concurrent with the development of distribution theory while also introducing the reader to basic statistical inference. In this way, the major stochastic processes are blended with coverage of probability laws, random variables, and distribution theory, equipping the reader to be a true problem solver and critical thinker.

Deliberately conversational in tone, Probability is written for students in junior- or senior-level probability courses majoring in mathematics, statistics, computer science, or engineering. The book offers a lucid and mathematicallysound introduction to how probability is used to model random behavior in the natural world. The text contains the following chapters:
_ Modeling
_ Sets and Functions
_ Probability Laws I: Building on the Axioms
_ Probability Laws II: Results of Conditioning
_ Random Variables and Stochastic Processes
_ Discrete Random Variables and Applications in Stochastic Processes
_ Continuous Random Variables and Applications in Stochastic Processes
_ Covariance and Correlation Among Random Variables

Included exercises cover a wealth of additional concepts, such as conditional independence, Simpson's paradox, acceptance sampling, geometric probability, simulation, exponential families of distributions, Jensen's inequality, and many non-standard probability distributions.

Produktdetails

• Verlag: Wiley & Sons
• 1. Auflage
• Seitenzahl: 488
• Erscheinungstermin: 1. August 2006
• Englisch
• Abmessung: 240mm x 161mm x 30mm
• Gewicht: 795g
• ISBN-13: 9780471458920
• ISBN-10: 0471458929
• Artikelnr.: 20871011

Autorenporträt

I love children of all ages, and love reading to children. It is such a joy watching them grow, not only physically, but socially and mentally as well. I have worked many years with children and have loved every minute. I am always amazed how fast they learn, and I love being a part of that learning process. I have worked in the classroom and in many summer camps for kids and teens, helping them build confidence and self-esteem to conquer their tasks. I have kids of my own that I have encouraged to succeed and be independent. I love seeing everyone succeed, especially in their courage, certainty, and self-esteem.I love sailing, photography, hiking, camping, scuba diving, motorcycle riding, and spending time with family. If it involves water, outdoors or family, then chances are I love it.

Inhaltsangabe

Preface. To the Student. To the Instructor. Coverage. Acknowledgments.
Chapter 1. Modeling. 1.1 Choice and Chance. 1.2 The Model Building Process.
1.3 Modeling in the Mathematical Sciences. 1.4 A First Look at a
Probability Model: The Random Walk. 1.5 Brief Applications of Random Walks.
Exercises. Chapter 2. Sets and Functions. 2.1 Operations with Sets. 2.2
Functions. 2.3 The Probability Function and the Axioms of Probability. 2.4
Equally Likely Sample Spaces and Counting Rules. Rules. Exercises. Chapter
3. Probility Laws I: Building on the Axioms. 3.1 The Complement Rule. 3.2
The Addition Rule. 3.3 Extensions and Additional Results. Exercises.
Chapter 4. Probility Laws II: Results of Conditioning. 4.1 Conditional
Probability and the Multiplication Rule. 4.2 Independent Events. 4.3 The
Theorem of Total Probabilities and Bayes' Rule. 4.4 Problems of Special
Interest: Effortful Illustrations of the Probability Laws. Exercises.
Chapter 5. Random Variables and Stochastic Processes. 5.1 Roles and Types
of Random Variables. 5.2 Expectation. 5.3 Roles, Types, and Characteristics
of Stochastic Processes. Exercises. Chapter 6. Discrete Random Variables
and Applications in Stochastic Processes. 6.1 The Bernoulli and Binomial
Models. 6.2 The Hypergeometric Model. 6.3 The Poisson Model. 6.4 The
Geometric and Negative Binomial. Models. Exercises. Chapter 7. Continuous
Random Variables and Applications in Stochastic Processes. 7.1 The
Continuous Uniform Model. 7.2 The Exponential Model. 7.3 The Gamma Model.
7.4 The Normal Model. Chapter 8. Covariance and Correlation Among Random
Variables. 8.1 Joint, Marginal and Conditional Distributions. 8.2
Covariance and Correlation. 8.3 Brief Examples and Illustrations in
Stochastic Processes and Times Series. Exercises. Bibliography. Tables.
Index.